The probability that a man will be alive 25 y | vedclass

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Question

(D) Let $A$ be the event that the man is alive and $B$ be the event that the wife is alive after $25$ years.
Given: $P(A) = 0.3$ and $P(B) = 0.4$.
T

Vedclass · Accepted Answer

$0.58$

Vedclass · Answer

(D) Let $A$ be the event that the man is alive and $B$ be the event that the wife is alive after $25$ years.
Given: $P(A) = 0.3$ and $P(B) = 0.4$.
The probability that the man is not alive is
$P(\bar{A}) = 1 - 0.3 = 0.7$.
The probability that the wife is not alive is
$P(\bar{B}) = 1 - 0.4 = 0.6$.
The probability that at least $1$ of them will be alive is given by
$1 - P(	ext{none of them is alive})$.
Since the events are independent,
$P(\bar{A} \cap \bar{B}) = P(\bar{A}) 	imes P(\bar{B}) = 0.7 	imes 0.6 = 0.42$.
Therefore, the required probability
$= 1 - 0.42 = 0.58$.

The probability that a man will be alive $25$ years hence is $0.3$ and the probability that his wife will be alive $25$ years hence is $0.4$. Find the probability that $25$ years hence, at least $1$ of them will be alive.

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